Given the conversation history \((q_1, q_2, \ldots , q_n)\)  and topic \(t\)  the first model proposed by [1]} can be described as:
\(& \texttt {Encoder:} & k = \bigcup _{x \in \lbrace q_{n-1}, q_n, t\rbrace }\textsc {TermVector}(x)\\& \texttt {Retriever:} & C = \textsc {InvertedIndexLookup}_7(k, \mathcal {KB}) \\& & \hspace{-28.45274pt} C^{\prime } = \lbrace \textsc {TransformerEnc}(\text{Title}(d) \,\frown \, \text{Paragraphs}(d)_1) | d \in C\rbrace  \\& \texttt {Aggregator} & \xi = \sum _{d^{\prime }\in C^{\prime }} d \times (d \cdot \textsc {TransformerEnc}(t) ) \\& \texttt {Model:} & o = \textsc {TransformerDec}(\textsc {TransformerEnc}(q)+a)\) 
